Gravitational spin Hamiltonians from the S matrix

TL;DR

This paper develops a novel computational approach using unitarity, recursion, and EFT techniques to derive spin-dependent Hamiltonians for inspiraling binaries, achieving higher-order accuracy and extending results to arbitrary massive objects.

Contribution

It introduces a new method combining unitarity, recursion, and EFT to efficiently compute high-order spin Hamiltonians for binary systems, including unknown terms for generic objects.

Findings

Reproduces spin-orbit interaction up to 2.5 PN order.

Derives leading order $S^2$ Hamiltonian at 3PN for arbitrary objects.

Obtains the $S^3$ Hamiltonian at 3.5PN for generic objects.

Abstract

We utilize generalized unitarity and recursion relations combined with effective field theory(EFT) techniques to compute spin dependent interaction terms for inspiralling binary systems in the post newtonian(PN) approximation. Using these methods offers great computational advantage over traditional techniques involving feynman diagrams, especially at higher orders in the PN expansion. As a specific example, we reproduce the spin-orbit interaction up to 2.5 PN order as also the leading order $S^2$(3PN) hamiltonian for an arbitrary massive object. We also obtain the unknown $S^3$(3.5PN) spin hamiltonian for an arbitrary massive object in terms of its low frequency linear response to gravitational perturbations, which was till now known only for a black hole. Furthermore, we derive the missing $S^4$ Hamiltonian at leading order(4PN) for an arbitrary massive object and establish that a minimal coupling of a massive elementary particle to gravity leads to a black hole structure. Finally, the Kerr metric is obtained as a series in $G_N$ by comparing the action of a test particle in the vicinity of a spinning black hole to the derived potential.